COMPASS Guided Operations Hub

User guide pages 2–9

Orientation

COMPASS is a discipline-adaptable curriculum analytics platform for curriculum review, advising, program analysis, assessment, and transfer evaluation. Mathematics examples serve as templates rather than constraints. In every discipline, courses can be modeled as graph nodes, course relationships as edges, and course-level concepts, skills, outcomes, or competencies as another connected layer.

Which tool should I use?

Standard two-pass operating sequence

Department onboarding sequence

Phase	Department action	Output
Prepare	Choose one program or concentration and appoint a small working group.	Course inventory, prerequisite/corequisite list, and shared folder for syllabi and outcomes.
Pilot	Analyze 2–4 strategically important courses.	Concept lists, dependency matrices, and early graph evidence.
Expand	Build the program graph and reconcile a shared vocabulary.	Program map, canonical concept/outcome list, and draft curriculum-map CSV.
Review	Use the AI assistants to interpret artifacts and draft the narrative.	Findings, Evidence, Next Steps; advising notes; transfer rationale.
Institutionalize	Assign update responsibility and version control.	Dated exports, stable file names, and a repeatable assessment cycle.

Role-based starting points

• Department chair or program coordinator: begin with Program Analyzer and Curriculum Map.
• Faculty member: begin with Concept Analyzer for courses you teach.
• Assessment coordinator: use Curriculum Map to connect concepts and outcomes to evidence.
• Advisor: use Program Analyzer to explain sequencing, gateways, and preparation needs.
• Transfer evaluator: use Course Transfer Analyzer with a current map and complete incoming syllabus.
• Administrative or student assistant: maintain names, versions, exports, and folders; curricular interpretation remains with faculty.

First 30 minutes

Time	Action	Expected result
0–5 min	Review the four core modules and choose one component.	A clear starting point.
5–10 min	Open the documentation for the selected component.	Required inputs and common mistakes are understood.
10–18 min	Run a small static-app example.	One structured artifact.
18–25 min	Export the artifact and open the corresponding AI assistant.	An evidence-grounded interpretation.
25–30 min	Write three bullets: Findings, Evidence, Next Steps.	A committee-ready note for review.

Quick access

User guide pages 12–13

Required inputs

Five-minute workflow

1. Open the Program Analyzer static app or the Program Map from the instructions page.
2. Load the appropriate state file or dataset.
3. Inspect the program graph and identify entry, feeder, hub, and terminal courses.
4. Review long chains, high-reach courses, missing metadata, and advising-sensitive points.
5. Export the graph and edge evidence, then use the AI assistant for review questions and narrative drafting.

How to read the output

Program review note template

Program Analyzer resources

User guide pages 10–11

Inputs and matrix convention

Five-minute workflow

1. Open the Concept Analyzer and enter or import the canonical concept list.
2. Mark only direct relationships; use ? where faculty judgment is unresolved.
3. Inspect the matrix, graph, analytics table, cycles, reachability, and bottleneck indicators.
4. Export the matrix and graph with the course, version, and date.
5. Use the AI assistant to draft Findings, Evidence, and Next Steps grounded in the export.

How to read the output

Minimal course-analysis report

Concept Analyzer resources

User guide pages 14–15

I/D/M matrix convention

Five-minute workflow

1. Open the Curriculum Mapper static app.
2. Load or enter the concept-by-course matrix.
3. Confirm that the concept column, course columns, and 0/1/2/3 values are clean.
4. Review I/D/M patterns for each concept.
5. Export the map and use the AI assistant to summarize gaps, redundancies, and progression concerns.

Curriculum-map reading patterns

Curriculum-map documentation template

Curriculum Map resources

User guide pages 16–17

Required inputs

Five-minute workflow

1. Open the COMPASS Transfer Analyzer.
2. Upload the official, current curriculum-map CSV.
3. Paste or upload the complete incoming syllabus.
4. Request concept mapping, overlap and weighted scores, ranked candidate courses, and diagnostics.
5. Review exact, near, and unmapped matches, missing local concepts, extra topics, ties, confidence, and the proposed recommendation.

Scoring notation

Let (L) be the official concept list, (A\subseteq L) the mapped incoming concepts, and (X_Y\subseteq L) the concepts taught in local course (Y). The overlap score is

When a tie requires additional evidence, use the curriculum-map levels:

Every strongest match, including ties, should be reported. Unmapped or invented concepts must not be counted in the score.

Transfer output checklist

Transfer review note template

Course Transfer resources

User guide pages 18–19 plus certification materials

Start Here documentation directory

Begin with documentation, produce a structured artifact, and then use the matching AI assistant to prepare review-ready documentation. Critical links are shown below with descriptive labels and visible URLs.

Orientation and ChatGPT access

COMPASS landing page

Open COMPASS landing pagehttps://vignonoussa.com/leveraging-ai-for-curriculum-mapping-and-analytics-to-enhance-academic-foundations-at-bsu/

BSU access request

Open BSU ChatGPT access requesthttps://ai-license-dashboard-bsu.replit.app/request

ChatGPT sign in

Open ChatGPThttps://chatgpt.com/

Plans and limits

Compare ChatGPT planshttps://chatgpt.com/pricing/

ChatGPT Edu overview

Open ChatGPT Edu overviewhttps://chatgpt.com/business/education/

OpenAI Help Center

Open Help Centerhttps://help.openai.com/

Downloads, data, tutorials, and formal archives

Program state files

State files for the Program Analyzer.

Download program state files ZIP

Curriculum map data

Data package for the Curriculum Mapper.

Download curriculum map data ZIP

Curriculum Mapper tutorial

Video walkthrough for the curriculum-map workflow.

Open Curriculum Mapper tutorial

Sample coverage CSV

Example matrix for testing the mapper.

Open sample coverage CSV

Concept Lean archive

Formal Lean 4/Mathlib companion archive for Concept Analyzer mathematics.

Open Concept Analyzer Lean archive

Program Lean package

Formal core and independent audit materials; theorem hypotheses and scope qualifications apply.

Open Program Analyzer Lean package

Transfer certification

Certificate, independent review, evidence, and a precise statement of scope.

Download Transfer Protocols certification

Transfer protocol paper

Source framework for the certified transfer-matching claims.

Open Transfer Protocols paper

ChatGPT access troubleshooting and support request checklist

Problem	Recommended action
AI link does not load	Sign in to ChatGPT, then reopen the COMPASS AI link.
Custom GPT unavailable	Confirm that the account plan or workspace supports custom GPTs and file uploads.
Upload fails	Try a smaller PDF, CSV, or XLSX; remove scanned image-only pages; or test with a text excerpt.
Output is too general	Upload the static-app export and require citations to specific matrix, graph, or table entries.
Sensitive data concern	Stop, de-identify the data, or use a synthetic example.
BSU access issue	Use the BSU access dashboard and include the COMPASS component you need.

Technical support. Contact Dr. Vignon Oussa with: (1) component name, (2) exact URL, (3) browser and device, (4) screenshot or copied error, (5) uploaded file type, and (6) the sequence of actions that produced the problem.

Reusable documentation templates

Lean certification: what is checked and what remains human

Program Analyzer formal map and independent audit

Certified core

• Typed program graphs, reachability, SCCs, sequencing, and longest paths.
• Risk-component algebra, uncertainty, trend, and what-if identities.
• Conditional bounds for bounded inputs and admissible weights.
• An abstract contraction theorem for recursive propagation.

Independent verification

• Lean 4.28.0 and Mathlib v4.28.0.
• lake build completed 8,037 jobs across all 11 modules.
• All 128 theorem declarations were replayed for axiom dependencies.
• Four non-fatal linter warnings occurred in Examples.lean.

Scope boundary

• The integrated endpoint consumes precomputed risk components.
• Range results require explicit boundedness and weight hypotheses.
• Recursive propagation is abstractly certified under \\(\\lVert A\\rVert<1\\).
• Raw-data validity, causality, statistical coverage, and threshold policy remain external.

Accurate public description. “A Lean-verified library for the deterministic graph-theoretic and algebraic core, with conditional range theorems.” The audit does not support calling the complete raw-data analyzer pipeline end-to-end certified.

Formal layer	Machine-checked content	Qualification
Typed foundation	Edge records, typed projections, observations, risk direction, clipping, and convex-combination lemmas.	Range conclusions require each theorem’s bounded-input and weight hypotheses.
Validation	Exact characterizations for missing endpoints, duplicate nodes/edges, and self-loops, plus additional predicates.	Not every advertised validation indicator has an if-and-only-if theorem.
Graph structure	Reachability, SCC/acyclicity, weak connectedness, corequisite contraction, and feasible block ranking.	The rank theorem produces natural-number levels, not an explicit topological list.
Structural metrics	Degree bounds, ancestor/descendant counts, longest paths, normalized depth, and classifications.	Normalized depth uses clipping where specified.
Risk algebra	Pooled rates, base risk, impact, exposures, bottleneck, pressure, fragility, combined scores, and sensitivities.	The [0,1] bounds require bounded components and nonnegative weights summing to one.
Recursive propagation	Existence and uniqueness for \\(x\\mapsto c+Ax\\) when \\(\\lVert A\\rVert<1\\).	No analyzer-specific \\(A=\\rho W\\) is instantiated, and no fixed-point [0,1] bound is proved.
Uncertainty and trends	Selected domain facts, shrinkage identities, interval-overlap symmetry, trends, and what-if sensitivities.	No certification of statistical coverage, Monte Carlo simulation, or every degenerate-input convention.
Determinism	The endpoint is deterministic for equal precomputed RunInput values.	runAnalyzer is not a raw-data-to-all-outputs composed theorem.

Audit identity: July 10, 2026; source SHA-256 2186E5AF9C6F7FC94A56F3CAFB06228558403F0795F01F6D0DC1CBCD3E17CEFF; public ZIP SHA-256 9AB3CDCF79D8C6B007F667F278CEA3609BC90DCE37E257FF71A77E848CC43076. All 29 endpoints in the archive’s Part XIV list exist; the manuscript was absent, so completeness against its external requirement list was not independently tested.

Transfer Protocols certification

Confirmed

• Consistent comparison of incoming concepts with local profiles.
• Both methods return every strongest match, including ties.
• Consistent relabeling leaves results unchanged.
• Adding concepts cannot lower an individual course’s score.
• A clear leader survives changes too small to erase its lead.

How checked

• Aristotle completed all 24 submitted statements.
• The complete result was checked again independently.
• All five source files passed.
• Every original statement was preserved.
• The package includes the review record and evidence.

Limits

• At least one local course is required for a match.
• A runner-up comparison requires at least two courses.
• Faculty confirm syllabus and profile accuracy.
• Equivalence, fairness, policy, and final credit remain human responsibilities.

Review area	Confirmed	Outside the certificate
Information setup	An agreed concept list and local-course profiles are used consistently.	Faculty confirm educational accuracy and meaning.
Course comparison	The two published comparison methods are applied consistently.	Departments select appropriate methods and settings.
Strongest matches	Every course tied for the strongest match is returned.	A strongest match is evidence, not an automatic decision.
Consistent labels	Consistent renaming does not change the result.	Splitting, combining, or redefining concepts requires review.
Additional concepts	Adding concepts cannot lower an individual course’s score.	Additional information may still change the first-ranked course.
Small changes	A clear leader remains first when edits cannot erase its lead.	Ties, inaccurate profiles, and major concept-list changes are excluded.
Repeatability	The repeatable version returns the protocol’s strongest-match set.	The live app and local review process were not certified.

Certification summary: checked July 10, 2026; 24 statements confirmed; five source files checked successfully; Aristotle’s result was independently rechecked.

Concept Analyzer formal companion

Representation and graphs

• The value alphabet \\(\\{0,1,\\tfrac12,?\\}\\) and schema.
• Strict, co-dependency, and uncertainty graph construction.
• The transpose convention \\(m_{ij}=1\\Rightarrow C_j\\to C_i\\).
• Topological order, cycles, SCCs, and block sequencing.
• Reachability, uncertainty intervals, transitive reduction, and export auditability.

Analytic layer

• Bounded normalized betweenness centrality.
• A unique PageRank probability fixed point for \\(0<\\alpha<1\\).
• A deterministic bottleneck score once coefficients are fixed.
• Formal degree, reachability, acyclicity, and betweenness examples.

What remains human

• Graph theory cannot prove a prerequisite judgment is pedagogically true.
• Domain experts validate the submitted matrix.
• Decimal PageRank and application-specific bottleneck values are reproducible numerical evaluations.

Formal contract. A faithful expert matrix implies correct finite graph-theoretic output. The certificate separates internal mathematical soundness from external curricular validity.

Layer	Certified content	Viewer-facing meaning
Representation	Unique strict, co-dependency, and uncertainty graphs.	The matrix has a precise graph meaning.
Transpose	Strict adjacency is the transpose of the strict-entry indicator.	A row concept requiring a column concept creates an edge from column to row.
Sequencing	Feasible strict orders exist exactly when the strict graph is acyclic.	All prerequisite arrows point forward in a valid order.
Cycles	A directed cycle rules out a strict linear order satisfying all stated dependencies.	A cycle is diagnostic evidence, not a software error.
Blocks	Co-dependency components can be sequenced as blocks when the block graph is acyclic.	Joint concepts are distinguished from strict prerequisites.
Reachability	Reach-in and reach-out count ancestors and supported descendants.	Gateway claims follow from graph paths.
Uncertainty	Lower and upper strict graphs bound completions of unresolved cells.	Unknown cells are not silently treated as facts.
Centrality	Betweenness, PageRank, removal effect, and bottleneck formulas are well-defined.	Scores are reproducible diagnostics, not curricular truths.
Export audit	A faithful export reconstructs the matrix and permits recomputation.	Reports can be checked outside the app.

The archive reports a clean lake build and no sorry, admit, added axiom, or unsafe workaround. Certified endpoints depend only on standard Lean/Mathlib principles: propext, Classical.choice, and Quot.sound.

Suggested citations and public acknowledgements

Program Analyzer: Oussa, V. Lean 4 formal companion for the Program Dependency and Risk Analyzer’s deterministic graph-theoretic and algebraic core, 2026. Independently audited July 10, 2026.

Concept Analyzer: Oussa, V. Lean 4 certification archive for concept dependency matrices and curricular analytics, formal companion archive, 2026.

Transfer Protocols: Oussa, V., and Shama, U. COMPASS Transfer Protocols Certification: independent assurance for the published transfer-matching rules, 2026. Independently checked July 10, 2026.

Funding acknowledgement. This work is supported by Bridgewater State University’s Academic Innovation Fund (InnovateBSU) through an Academic Innovation Project Grant (AY 2025–2026) for the project “Leveraging AI for Curriculum Mapping and Analytics to Enhance Academic Foundations at BSU.”

Dr. Vignon Oussa

COMPASS development, maintenance, public curriculum-analytics ecosystem, and documentation framework.

Dr. Uma Shama

Strategic alignment, communication framing, and coauthorship of the Transfer Protocols framework.

Chigo Adigwe

Workflow requirements and usability feedback.

Lalitha Bhavanand

Implementation feedback and documentation refinement.

Nicole Medeiros

COMPASS documentation and project deliverables.

Accessibility and usability checks for editors

• Use descriptive link text and keep visible URLs for critical external resources.
• Do not rely on color alone; labels, headings, and table cells carry the interpretation.
• Keep diagrams simple, readable, and free of clipped labels.
• Add alt text or figure descriptions when adding screenshots or figures.
• Maintain a clear heading structure and PDF bookmarks after conversion.
• Prefer short paragraphs, meaningful headings, and scannable tables.
• Keep versioned source files and verify keyboard, mobile, reduced-motion, and print behavior before publication.